Briefly mix the vinegar, salt, and optional mustard with an immersion blender, food processor or blender, or with a fork or wire whisk. Slowly add the oil in a stream (drop by drop if whisking) until an emulsion forms or just whisk everything together briefly. Add the remaining oil faster, but still in a stream. Taste to adjust salt and add more oil or viengar if needed. Add the shallots and pepper. This is best made fresh, but will keep, refrigerated for a few days; bring back to room temperature before using.

To make a small amount of Basic Vinaigrette: Combine 1 to 1 1/2 tablespoons vinegar, 1/4 teaspoon salt, 1/2 teaspoon mustard, 3 to 4 tablespoons oil, and 1/2 teaspoon minced shallots as above. Add pepper, then taste and add more vinegar, salt, or oil as necessary.